LMFDB - Embedded newform 1014.2.b.g.337.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(337,1014)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1014.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.153664.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} + 6x^{2} + 1 $ x^6 + 5x^4 + 6x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.5
Root			$1.80194i$ of defining polynomial
Character	$\chi$	$=$	1014.337
Dual form			1014.2.b.g.337.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +0.356896i q^{5} +1.00000i q^{6} -4.04892i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +0.356896i q^{5} +1.00000i q^{6} -4.04892i q^{7} -1.00000i q^{8} +1.00000 q^{9} -0.356896 q^{10} +0.911854i q^{11} -1.00000 q^{12} +4.04892 q^{14} +0.356896i q^{15} +1.00000 q^{16} +2.09783 q^{17} +1.00000i q^{18} -4.98792i q^{19} -0.356896i q^{20} -4.04892i q^{21} -0.911854 q^{22} -8.49396 q^{23} -1.00000i q^{24} +4.87263 q^{25} +1.00000 q^{27} +4.04892i q^{28} +8.51573 q^{29} -0.356896 q^{30} -10.7899i q^{31} +1.00000i q^{32} +0.911854i q^{33} +2.09783i q^{34} +1.44504 q^{35} -1.00000 q^{36} +0.615957i q^{37} +4.98792 q^{38} +0.356896 q^{40} -7.60388i q^{41} +4.04892 q^{42} +6.27413 q^{43} -0.911854i q^{44} +0.356896i q^{45} -8.49396i q^{46} -1.78017i q^{47} +1.00000 q^{48} -9.39373 q^{49} +4.87263i q^{50} +2.09783 q^{51} +10.4112 q^{53} +1.00000i q^{54} -0.325437 q^{55} -4.04892 q^{56} -4.98792i q^{57} +8.51573i q^{58} +6.04892i q^{59} -0.356896i q^{60} -3.10992 q^{61} +10.7899 q^{62} -4.04892i q^{63} -1.00000 q^{64} -0.911854 q^{66} +13.5797i q^{67} -2.09783 q^{68} -8.49396 q^{69} +1.44504i q^{70} +11.4819i q^{71} -1.00000i q^{72} -0.533188i q^{73} -0.615957 q^{74} +4.87263 q^{75} +4.98792i q^{76} +3.69202 q^{77} -11.7071 q^{79} +0.356896i q^{80} +1.00000 q^{81} +7.60388 q^{82} -6.49934i q^{83} +4.04892i q^{84} +0.748709i q^{85} +6.27413i q^{86} +8.51573 q^{87} +0.911854 q^{88} +6.49396i q^{89} -0.356896 q^{90} +8.49396 q^{92} -10.7899i q^{93} +1.78017 q^{94} +1.78017 q^{95} +1.00000i q^{96} -1.96077i q^{97} -9.39373i q^{98} +0.911854i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9	$ 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9} + 6 q^{10} - 6 q^{12} + 6 q^{14} + 6 q^{16} - 24 q^{17} + 2 q^{22} - 32 q^{23} - 4 q^{25} + 6 q^{27} + 26 q^{29} + 6 q^{30} + 8 q^{35} - 6 q^{36} - 8 q^{38} - 6 q^{40} + 6 q^{42} + 16 q^{43} + 6 q^{48} + 8 q^{49} - 24 q^{51} + 30 q^{53} - 44 q^{55} - 6 q^{56} - 20 q^{61} + 18 q^{62} - 6 q^{64} + 2 q^{66} + 24 q^{68} - 32 q^{69} - 24 q^{74} - 4 q^{75} + 12 q^{77} - 10 q^{79} + 6 q^{81} + 28 q^{82} + 26 q^{87} - 2 q^{88} + 6 q^{90} + 32 q^{92} + 8 q^{94} + 8 q^{95}+O(q^{100}) $ 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9 + 6 * q^10 - 6 * q^12 + 6 * q^14 + 6 * q^16 - 24 * q^17 + 2 * q^22 - 32 * q^23 - 4 * q^25 + 6 * q^27 + 26 * q^29 + 6 * q^30 + 8 * q^35 - 6 * q^36 - 8 * q^38 - 6 * q^40 + 6 * q^42 + 16 * q^43 + 6 * q^48 + 8 * q^49 - 24 * q^51 + 30 * q^53 - 44 * q^55 - 6 * q^56 - 20 * q^61 + 18 * q^62 - 6 * q^64 + 2 * q^66 + 24 * q^68 - 32 * q^69 - 24 * q^74 - 4 * q^75 + 12 * q^77 - 10 * q^79 + 6 * q^81 + 28 * q^82 + 26 * q^87 - 2 * q^88 + 6 * q^90 + 32 * q^92 + 8 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.00000	−0.500000
$5$	0.356896i	0.159609i	0.996811	+	0.0798043i	$0.0254296\pi$
$5$	0.356896i	0.159609i	−0.996811	+	0.0798043i	$0.974570\pi$
$6$	1.00000i	0.408248i
$7$	− 4.04892i	− 1.53035i	−0.643824	−	0.765173i	$-0.722653\pi$
$7$	− 4.04892i	− 1.53035i	0.643824	−	0.765173i	$-0.277347\pi$
$8$	− 1.00000i	− 0.353553i
$9$	1.00000	0.333333
$10$	−0.356896	−0.112860
$11$	0.911854i	0.274934i	0.990506	+	0.137467i	$0.0438962\pi$
$11$	0.911854i	0.274934i	−0.990506	+	0.137467i	$0.956104\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	4.04892	1.08212
$15$	0.356896i	0.0921501i
$16$	1.00000	0.250000
$17$	2.09783	0.508800	0.254400	−	0.967099i	$-0.418122\pi$
$17$	2.09783	0.508800	0.254400	+	0.967099i	$0.418122\pi$
$18$	1.00000i	0.235702i
$19$	− 4.98792i	− 1.14431i	−0.820147	−	0.572153i	$-0.806108\pi$
$19$	− 4.98792i	− 1.14431i	0.820147	−	0.572153i	$-0.193892\pi$
$20$	− 0.356896i	− 0.0798043i
$21$	− 4.04892i	− 0.883546i
$22$	−0.911854	−0.194408
$23$	−8.49396	−1.77111	−0.885556	−	0.464532i	$-0.846223\pi$
$23$	−8.49396	−1.77111	−0.885556	+	0.464532i	$0.846223\pi$
$24$	− 1.00000i	− 0.204124i
$25$	4.87263	0.974525
$26$	0	0
$27$	1.00000	0.192450
$28$	4.04892i	0.765173i
$29$	8.51573	1.58133	0.790666	−	0.612248i	$-0.209735\pi$
$29$	8.51573	1.58133	0.790666	+	0.612248i	$0.209735\pi$
$30$	−0.356896	−0.0651600
$31$	− 10.7899i	− 1.93792i	−0.247227	−	0.968958i	$-0.579519\pi$
$31$	− 10.7899i	− 1.93792i	0.247227	−	0.968958i	$-0.420481\pi$
$32$	1.00000i	0.176777i
$33$	0.911854i	0.158733i
$34$	2.09783i	0.359776i
$35$	1.44504	0.244257
$36$	−1.00000	−0.166667
$37$	0.615957i	0.101263i	0.998717	+	0.0506314i	$0.0161234\pi$
$37$	0.615957i	0.101263i	−0.998717	+	0.0506314i	$0.983877\pi$
$38$	4.98792	0.809147
$39$	0	0
$40$	0.356896	0.0564302
$41$	− 7.60388i	− 1.18753i	−0.804640	−	0.593763i	$-0.797642\pi$
$41$	− 7.60388i	− 1.18753i	0.804640	−	0.593763i	$-0.202358\pi$
$42$	4.04892	0.624762
$43$	6.27413	0.956795	0.478398	−	0.878143i	$-0.341218\pi$
$43$	6.27413	0.956795	0.478398	+	0.878143i	$0.341218\pi$
$44$	− 0.911854i	− 0.137467i
$45$	0.356896i	0.0532029i
$46$	− 8.49396i	− 1.25237i
$47$	− 1.78017i	− 0.259664i	−0.991536	−	0.129832i	$-0.958556\pi$
$47$	− 1.78017i	− 0.259664i	0.991536	−	0.129832i	$-0.0414438\pi$
$48$	1.00000	0.144338
$49$	−9.39373	−1.34196
$50$	4.87263i	0.689093i
$51$	2.09783	0.293756
$52$	0	0
$53$	10.4112	1.43009	0.715043	−	0.699080i	$-0.246407\pi$
$53$	10.4112	1.43009	0.715043	+	0.699080i	$0.246407\pi$
$54$	1.00000i	0.136083i
$55$	−0.325437	−0.0438819
$56$	−4.04892	−0.541059
$57$	− 4.98792i	− 0.660666i
$58$	8.51573i	1.11817i
$59$	6.04892i	0.787502i	0.919217	+	0.393751i	$0.128823\pi$
$59$	6.04892i	0.787502i	−0.919217	+	0.393751i	$0.871177\pi$
$60$	− 0.356896i	− 0.0460751i
$61$	−3.10992	−0.398184	−0.199092	−	0.979981i	$-0.563799\pi$
$61$	−3.10992	−0.398184	−0.199092	+	0.979981i	$0.563799\pi$
$62$	10.7899	1.37031
$63$	− 4.04892i	− 0.510116i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−0.911854	−0.112241
$67$	13.5797i	1.65903i	0.558487	+	0.829513i	$0.311382\pi$
$67$	13.5797i	1.65903i	−0.558487	+	0.829513i	$0.688618\pi$
$68$	−2.09783	−0.254400
$69$	−8.49396	−1.02255
$70$	1.44504i	0.172716i
$71$	11.4819i	1.36265i	0.731982	+	0.681324i	$0.238596\pi$
$71$	11.4819i	1.36265i	−0.731982	+	0.681324i	$0.761404\pi$
$72$	− 1.00000i	− 0.117851i
$73$	− 0.533188i	− 0.0624049i	−0.999513	−	0.0312025i	$-0.990066\pi$
$73$	− 0.533188i	− 0.0624049i	0.999513	−	0.0312025i	$-0.00993366\pi$
$74$	−0.615957	−0.0716036
$75$	4.87263	0.562642
$76$	4.98792i	0.572153i
$77$	3.69202	0.420745
$78$	0	0
$79$	−11.7071	−1.31715	−0.658575	−	0.752515i	$-0.728841\pi$
$79$	−11.7071	−1.31715	−0.658575	+	0.752515i	$0.728841\pi$
$80$	0.356896i	0.0399022i
$81$	1.00000	0.111111
$82$	7.60388	0.839708
$83$	− 6.49934i	− 0.713395i	−0.934220	−	0.356697i	$-0.883903\pi$
$83$	− 6.49934i	− 0.713395i	0.934220	−	0.356697i	$-0.116097\pi$
$84$	4.04892i	0.441773i
$85$	0.748709i	0.0812088i
$86$	6.27413i	0.676556i
$87$	8.51573	0.912982
$88$	0.911854	0.0972040
$89$	6.49396i	0.688358i	0.938904	+	0.344179i	$0.111843\pi$
$89$	6.49396i	0.688358i	−0.938904	+	0.344179i	$0.888157\pi$
$90$	−0.356896	−0.0376201
$91$	0	0
$92$	8.49396	0.885556
$93$	− 10.7899i	− 1.11886i
$94$	1.78017	0.183610
$95$	1.78017	0.182641
$96$	1.00000i	0.102062i
$97$	− 1.96077i	− 0.199086i	−0.995033	−	0.0995431i	$-0.968262\pi$
$97$	− 1.96077i	− 0.199086i	0.995033	−	0.0995431i	$-0.0317381\pi$
$98$	− 9.39373i	− 0.948910i
$99$	0.911854i	0.0916448i
$100$	−4.87263	−0.487263
$101$	−6.98254	−0.694789	−0.347394	−	0.937719i	$-0.612933\pi$
$101$	−6.98254	−0.694789	−0.347394	+	0.937719i	$0.612933\pi$
$102$	2.09783i	0.207717i
$103$	−4.94869	−0.487609	−0.243804	−	0.969824i	$-0.578396\pi$
$103$	−4.94869	−0.487609	−0.243804	+	0.969824i	$0.578396\pi$
$104$	0	0
$105$	1.44504	0.141022
$106$	10.4112i	1.01122i
$107$	−4.26875	−0.412676	−0.206338	−	0.978481i	$-0.566155\pi$
$107$	−4.26875	−0.412676	−0.206338	+	0.978481i	$0.566155\pi$
$108$	−1.00000	−0.0962250
$109$	− 6.21983i	− 0.595752i	−0.954605	−	0.297876i	$-0.903722\pi$
$109$	− 6.21983i	− 0.595752i	0.954605	−	0.297876i	$-0.0962782\pi$
$110$	− 0.325437i	− 0.0310292i
$111$	0.615957i	0.0584641i
$112$	− 4.04892i	− 0.382587i
$113$	12.9879	1.22180	0.610900	−	0.791708i	$-0.290808\pi$
$113$	12.9879	1.22180	0.610900	+	0.791708i	$0.290808\pi$
$114$	4.98792	0.467161
$115$	− 3.03146i	− 0.282685i
$116$	−8.51573	−0.790666
$117$	0	0
$118$	−6.04892	−0.556848
$119$	− 8.49396i	− 0.778640i
$120$	0.356896	0.0325800
$121$	10.1685	0.924411
$122$	− 3.10992i	− 0.281559i
$123$	− 7.60388i	− 0.685618i
$124$	10.7899i	0.968958i
$125$	3.52350i	0.315151i
$126$	4.04892	0.360706
$127$	−9.22282	−0.818393	−0.409196	−	0.912446i	$-0.634191\pi$
$127$	−9.22282	−0.818393	−0.409196	+	0.912446i	$0.634191\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	6.27413	0.552406
$130$	0	0
$131$	−14.5526	−1.27146	−0.635732	−	0.771910i	$-0.719302\pi$
$131$	−14.5526	−1.27146	−0.635732	+	0.771910i	$0.719302\pi$
$132$	− 0.911854i	− 0.0793667i
$133$	−20.1957	−1.75119
$134$	−13.5797	−1.17311
$135$	0.356896i	0.0307167i
$136$	− 2.09783i	− 0.179888i
$137$	15.4034i	1.31600i	0.753017	+	0.658002i	$0.228598\pi$
$137$	15.4034i	1.31600i	−0.753017	+	0.658002i	$0.771402\pi$
$138$	− 8.49396i	− 0.723054i
$139$	2.71379	0.230181	0.115090	−	0.993355i	$-0.463284\pi$
$139$	2.71379	0.230181	0.115090	+	0.993355i	$0.463284\pi$
$140$	−1.44504	−0.122128
$141$	− 1.78017i	− 0.149917i
$142$	−11.4819	−0.963538
$143$	0	0
$144$	1.00000	0.0833333
$145$	3.03923i	0.252394i
$146$	0.533188	0.0441269
$147$	−9.39373	−0.774782
$148$	− 0.615957i	− 0.0506314i
$149$	− 14.7356i	− 1.20718i	−0.797293	−	0.603592i	$-0.793736\pi$
$149$	− 14.7356i	− 1.20718i	0.797293	−	0.603592i	$-0.206264\pi$
$150$	4.87263i	0.397848i
$151$	15.8213i	1.28752i	0.765227	+	0.643760i	$0.222627\pi$
$151$	15.8213i	1.28752i	−0.765227	+	0.643760i	$0.777373\pi$
$152$	−4.98792	−0.404574
$153$	2.09783	0.169600
$154$	3.69202i	0.297512i
$155$	3.85086	0.309308
$156$	0	0
$157$	−4.27413	−0.341112	−0.170556	−	0.985348i	$-0.554556\pi$
$157$	−4.27413	−0.341112	−0.170556	+	0.985348i	$0.554556\pi$
$158$	− 11.7071i	− 0.931366i
$159$	10.4112	0.825661
$160$	−0.356896	−0.0282151
$161$	34.3913i	2.71042i
$162$	1.00000i	0.0785674i
$163$	0.317667i	0.0248816i	0.999923	+	0.0124408i	$0.00396013\pi$
$163$	0.317667i	0.0248816i	−0.999923	+	0.0124408i	$0.996040\pi$
$164$	7.60388i	0.593763i
$165$	−0.325437	−0.0253352
$166$	6.49934	0.504446
$167$	− 12.3612i	− 0.956539i	−0.878213	−	0.478269i	$-0.841264\pi$
$167$	− 12.3612i	− 0.956539i	0.878213	−	0.478269i	$-0.158736\pi$
$168$	−4.04892	−0.312381
$169$	0	0
$170$	−0.748709	−0.0574233
$171$	− 4.98792i	− 0.381436i
$172$	−6.27413	−0.478398
$173$	17.0640	1.29735	0.648675	−	0.761065i	$-0.275323\pi$
$173$	17.0640	1.29735	0.648675	+	0.761065i	$0.275323\pi$
$174$	8.51573i	0.645576i
$175$	− 19.7289i	− 1.49136i
$176$	0.911854i	0.0687336i
$177$	6.04892i	0.454664i
$178$	−6.49396	−0.486743
$179$	24.9681	1.86620	0.933100	−	0.359616i	$-0.117092\pi$
$179$	24.9681	1.86620	0.933100	+	0.359616i	$0.117092\pi$
$180$	− 0.356896i	− 0.0266014i
$181$	−5.26205	−0.391125	−0.195562	−	0.980691i	$-0.562653\pi$
$181$	−5.26205	−0.391125	−0.195562	+	0.980691i	$0.562653\pi$
$182$	0	0
$183$	−3.10992	−0.229892
$184$	8.49396i	0.626183i
$185$	−0.219833	−0.0161624
$186$	10.7899	0.791151
$187$	1.91292i	0.139886i
$188$	1.78017i	0.129832i
$189$	− 4.04892i	− 0.294515i
$190$	1.78017i	0.129147i
$191$	10.5375	0.762467	0.381233	−	0.924479i	$-0.375499\pi$
$191$	10.5375	0.762467	0.381233	+	0.924479i	$0.375499\pi$
$192$	−1.00000	−0.0721688
$193$	− 3.42758i	− 0.246723i	−0.992362	−	0.123361i	$-0.960633\pi$
$193$	− 3.42758i	− 0.246723i	0.992362	−	0.123361i	$-0.0393674\pi$
$194$	1.96077	0.140775
$195$	0	0
$196$	9.39373	0.670981
$197$	3.77479i	0.268943i	0.990917	+	0.134471i	$0.0429336\pi$
$197$	3.77479i	0.268943i	−0.990917	+	0.134471i	$0.957066\pi$
$198$	−0.911854	−0.0648026
$199$	−17.9541	−1.27273	−0.636365	−	0.771388i	$-0.719563\pi$
$199$	−17.9541	−1.27273	−0.636365	+	0.771388i	$0.719563\pi$
$200$	− 4.87263i	− 0.344547i
$201$	13.5797i	0.957839i
$202$	− 6.98254i	− 0.491290i
$203$	− 34.4795i	− 2.41999i
$204$	−2.09783	−0.146878
$205$	2.71379	0.189539
$206$	− 4.94869i	− 0.344792i
$207$	−8.49396	−0.590371
$208$	0	0
$209$	4.54825	0.314609
$210$	1.44504i	0.0997174i
$211$	−12.5375	−0.863117	−0.431559	−	0.902085i	$-0.642036\pi$
$211$	−12.5375	−0.863117	−0.431559	+	0.902085i	$0.642036\pi$
$212$	−10.4112	−0.715043
$213$	11.4819i	0.786725i
$214$	− 4.26875i	− 0.291806i
$215$	2.23921i	0.152713i
$216$	− 1.00000i	− 0.0680414i
$217$	−43.6872	−2.96568
$218$	6.21983	0.421260
$219$	− 0.533188i	− 0.0360295i
$220$	0.325437	0.0219410
$221$	0	0
$222$	−0.615957	−0.0413403
$223$	5.42758i	0.363458i	0.983349	+	0.181729i	$0.0581693\pi$
$223$	5.42758i	0.363458i	−0.983349	+	0.181729i	$0.941831\pi$
$224$	4.04892	0.270530
$225$	4.87263	0.324842
$226$	12.9879i	0.863943i
$227$	16.5767i	1.10024i	0.835087	+	0.550118i	$0.185417\pi$
$227$	16.5767i	1.10024i	−0.835087	+	0.550118i	$0.814583\pi$
$228$	4.98792i	0.330333i
$229$	23.8780i	1.57790i	0.614456	+	0.788951i	$0.289376\pi$
$229$	23.8780i	1.57790i	−0.614456	+	0.788951i	$0.710624\pi$
$230$	3.03146	0.199888
$231$	3.69202	0.242917
$232$	− 8.51573i	− 0.559085i
$233$	−13.9952	−0.916857	−0.458428	−	0.888731i	$-0.651587\pi$
$233$	−13.9952	−0.916857	−0.458428	+	0.888731i	$0.651587\pi$
$234$	0	0
$235$	0.635334	0.0414446
$236$	− 6.04892i	− 0.393751i
$237$	−11.7071	−0.760457
$238$	8.49396	0.550582
$239$	13.2862i	0.859413i	0.902969	+	0.429707i	$0.141383\pi$
$239$	13.2862i	0.859413i	−0.902969	+	0.429707i	$0.858617\pi$
$240$	0.356896i	0.0230375i
$241$	− 10.4789i	− 0.675005i	−0.941325	−	0.337502i	$-0.890418\pi$
$241$	− 10.4789i	− 0.675005i	0.941325	−	0.337502i	$-0.109582\pi$
$242$	10.1685i	0.653657i
$243$	1.00000	0.0641500
$244$	3.10992	0.199092
$245$	− 3.35258i	− 0.214189i
$246$	7.60388	0.484805
$247$	0	0
$248$	−10.7899	−0.685157
$249$	− 6.49934i	− 0.411879i
$250$	−3.52350	−0.222846
$251$	−3.48725	−0.220114	−0.110057	−	0.993925i	$-0.535103\pi$
$251$	−3.48725	−0.220114	−0.110057	+	0.993925i	$0.535103\pi$
$252$	4.04892i	0.255058i
$253$	− 7.74525i	− 0.486940i
$254$	− 9.22282i	− 0.578691i
$255$	0.748709i	0.0468859i
$256$	1.00000	0.0625000
$257$	−6.53750	−0.407798	−0.203899	−	0.978992i	$-0.565361\pi$
$257$	−6.53750	−0.407798	−0.203899	+	0.978992i	$0.565361\pi$
$258$	6.27413i	0.390610i
$259$	2.49396	0.154967
$260$	0	0
$261$	8.51573	0.527110
$262$	− 14.5526i	− 0.899060i
$263$	8.01938	0.494496	0.247248	−	0.968952i	$-0.420474\pi$
$263$	8.01938	0.494496	0.247248	+	0.968952i	$0.420474\pi$
$264$	0.911854	0.0561207
$265$	3.71571i	0.228254i
$266$	− 20.1957i	− 1.23828i
$267$	6.49396i	0.397424i
$268$	− 13.5797i	− 0.829513i
$269$	−27.6732	−1.68727	−0.843633	−	0.536920i	$-0.819588\pi$
$269$	−27.6732	−1.68727	−0.843633	+	0.536920i	$0.819588\pi$
$270$	−0.356896	−0.0217200
$271$	− 14.7289i	− 0.894714i	−0.894355	−	0.447357i	$-0.852365\pi$
$271$	− 14.7289i	− 0.894714i	0.894355	−	0.447357i	$-0.147635\pi$
$272$	2.09783	0.127200
$273$	0	0
$274$	−15.4034	−0.930555
$275$	4.44312i	0.267930i
$276$	8.49396	0.511276
$277$	−3.26205	−0.195997	−0.0979986	−	0.995187i	$-0.531244\pi$
$277$	−3.26205	−0.195997	−0.0979986	+	0.995187i	$0.531244\pi$
$278$	2.71379i	0.162762i
$279$	− 10.7899i	− 0.645972i
$280$	− 1.44504i	− 0.0863578i
$281$	− 7.72587i	− 0.460887i	−0.973086	−	0.230443i	$-0.925982\pi$
$281$	− 7.72587i	− 0.460887i	0.973086	−	0.230443i	$-0.0740177\pi$
$282$	1.78017	0.106007
$283$	19.7802	1.17581	0.587904	−	0.808930i	$-0.299953\pi$
$283$	19.7802	1.17581	0.587904	+	0.808930i	$0.299953\pi$
$284$	− 11.4819i	− 0.681324i
$285$	1.78017	0.105448
$286$	0	0
$287$	−30.7875	−1.81733
$288$	1.00000i	0.0589256i
$289$	−12.5991	−0.741123
$290$	−3.03923	−0.178470
$291$	− 1.96077i	− 0.114942i
$292$	0.533188i	0.0312025i
$293$	12.9119i	0.754319i	0.926148	+	0.377159i	$0.123099\pi$
$293$	12.9119i	0.754319i	−0.926148	+	0.377159i	$0.876901\pi$
$294$	− 9.39373i	− 0.547854i
$295$	−2.15883	−0.125692
$296$	0.615957	0.0358018
$297$	0.911854i	0.0529111i
$298$	14.7356	0.853608
$299$	0	0
$300$	−4.87263	−0.281321
$301$	− 25.4034i	− 1.46423i
$302$	−15.8213	−0.910414
$303$	−6.98254	−0.401137
$304$	− 4.98792i	− 0.286077i
$305$	− 1.10992i	− 0.0635536i
$306$	2.09783i	0.119925i
$307$	− 19.9651i	− 1.13947i	−0.821829	−	0.569734i	$-0.807046\pi$
$307$	− 19.9651i	− 1.13947i	0.821829	−	0.569734i	$-0.192954\pi$
$308$	−3.69202	−0.210372
$309$	−4.94869	−0.281521
$310$	3.85086i	0.218714i
$311$	−13.4819	−0.764487	−0.382244	−	0.924062i	$-0.624848\pi$
$311$	−13.4819	−0.764487	−0.382244	+	0.924062i	$0.624848\pi$
$312$	0	0
$313$	12.9245	0.730537	0.365269	−	0.930902i	$-0.380977\pi$
$313$	12.9245	0.730537	0.365269	+	0.930902i	$0.380977\pi$
$314$	− 4.27413i	− 0.241203i
$315$	1.44504	0.0814189
$316$	11.7071	0.658575
$317$	− 11.8726i	− 0.666833i	−0.942780	−	0.333417i	$-0.891798\pi$
$317$	− 11.8726i	− 0.666833i	0.942780	−	0.333417i	$-0.108202\pi$
$318$	10.4112i	0.583831i
$319$	7.76510i	0.434762i
$320$	− 0.356896i	− 0.0199511i
$321$	−4.26875	−0.238258
$322$	−34.3913	−1.91655
$323$	− 10.4638i	− 0.582223i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−0.317667	−0.0175940
$327$	− 6.21983i	− 0.343958i
$328$	−7.60388	−0.419854
$329$	−7.20775	−0.397376
$330$	− 0.325437i	− 0.0179147i
$331$	10.2392i	0.562798i	0.959591	+	0.281399i	$0.0907984\pi$
$331$	10.2392i	0.562798i	−0.959591	+	0.281399i	$0.909202\pi$
$332$	6.49934i	0.356697i
$333$	0.615957i	0.0337542i
$334$	12.3612	0.676375
$335$	−4.84654	−0.264795
$336$	− 4.04892i	− 0.220887i
$337$	−1.44935	−0.0789513	−0.0394757	−	0.999221i	$-0.512569\pi$
$337$	−1.44935	−0.0789513	−0.0394757	+	0.999221i	$0.512569\pi$
$338$	0	0
$339$	12.9879	0.705407
$340$	− 0.748709i	− 0.0406044i
$341$	9.83877	0.532799
$342$	4.98792	0.269716
$343$	9.69202i	0.523320i
$344$	− 6.27413i	− 0.338278i
$345$	− 3.03146i	− 0.163208i
$346$	17.0640i	0.917365i
$347$	6.84117	0.367253	0.183627	−	0.982996i	$-0.441216\pi$
$347$	6.84117	0.367253	0.183627	+	0.982996i	$0.441216\pi$
$348$	−8.51573	−0.456491
$349$	34.3370i	1.83802i	0.394234	+	0.919010i	$0.371010\pi$
$349$	34.3370i	1.83802i	−0.394234	+	0.919010i	$0.628990\pi$
$350$	19.7289	1.05455
$351$	0	0
$352$	−0.911854	−0.0486020
$353$	26.0495i	1.38648i	0.720709	+	0.693238i	$0.243816\pi$
$353$	26.0495i	1.38648i	−0.720709	+	0.693238i	$0.756184\pi$
$354$	−6.04892	−0.321496
$355$	−4.09783	−0.217490
$356$	− 6.49396i	− 0.344179i
$357$	− 8.49396i	− 0.449548i
$358$	24.9681i	1.31960i
$359$	− 8.49396i	− 0.448294i	−0.974555	−	0.224147i	$-0.928040\pi$
$359$	− 8.49396i	− 0.448294i	0.974555	−	0.224147i	$-0.0719596\pi$
$360$	0.356896	0.0188101
$361$	−5.87933	−0.309438
$362$	− 5.26205i	− 0.276567i
$363$	10.1685	0.533709
$364$	0	0
$365$	0.190293	0.00996037
$366$	− 3.10992i	− 0.162558i
$367$	27.4523	1.43300	0.716500	−	0.697587i	$-0.245743\pi$
$367$	27.4523	1.43300	0.716500	+	0.697587i	$0.245743\pi$
$368$	−8.49396	−0.442778
$369$	− 7.60388i	− 0.395842i
$370$	− 0.219833i	− 0.0114285i
$371$	− 42.1540i	− 2.18853i
$372$	10.7899i	0.559428i
$373$	26.6219	1.37843	0.689216	−	0.724556i	$-0.257955\pi$
$373$	26.6219	1.37843	0.689216	+	0.724556i	$0.257955\pi$
$374$	−1.91292	−0.0989147
$375$	3.52350i	0.181953i
$376$	−1.78017	−0.0918051
$377$	0	0
$378$	4.04892	0.208254
$379$	11.6474i	0.598288i	0.954208	+	0.299144i	$0.0967010\pi$
$379$	11.6474i	0.598288i	−0.954208	+	0.299144i	$0.903299\pi$
$380$	−1.78017	−0.0913207
$381$	−9.22282	−0.472499
$382$	10.5375i	0.539145i
$383$	10.5181i	0.537451i	0.963217	+	0.268725i	$0.0866024\pi$
$383$	10.5181i	0.537451i	−0.963217	+	0.268725i	$0.913398\pi$
$384$	− 1.00000i	− 0.0510310i
$385$	1.31767i	0.0671545i
$386$	3.42758	0.174459
$387$	6.27413	0.318932
$388$	1.96077i	0.0995431i
$389$	9.25965	0.469483	0.234742	−	0.972058i	$-0.424576\pi$
$389$	9.25965	0.469483	0.234742	+	0.972058i	$0.424576\pi$
$390$	0	0
$391$	−17.8189	−0.901142
$392$	9.39373i	0.474455i
$393$	−14.5526	−0.734080
$394$	−3.77479	−0.190171
$395$	− 4.17821i	− 0.210229i
$396$	− 0.911854i	− 0.0458224i
$397$	− 14.5133i	− 0.728403i	−0.931320	−	0.364202i	$-0.881342\pi$
$397$	− 14.5133i	− 0.728403i	0.931320	−	0.364202i	$-0.118658\pi$
$398$	− 17.9541i	− 0.899956i
$399$	−20.1957	−1.01105
$400$	4.87263	0.243631
$401$	38.8418i	1.93966i	0.243773	+	0.969832i	$0.421615\pi$
$401$	38.8418i	1.93966i	−0.243773	+	0.969832i	$0.578385\pi$
$402$	−13.5797	−0.677294
$403$	0	0
$404$	6.98254	0.347394
$405$	0.356896i	0.0177343i
$406$	34.4795	1.71119
$407$	−0.561663	−0.0278406
$408$	− 2.09783i	− 0.103858i
$409$	33.9221i	1.67734i	0.544639	+	0.838671i	$0.316667\pi$
$409$	33.9221i	1.67734i	−0.544639	+	0.838671i	$0.683333\pi$
$410$	2.71379i	0.134025i
$411$	15.4034i	0.759795i
$412$	4.94869	0.243804
$413$	24.4916	1.20515
$414$	− 8.49396i	− 0.417455i
$415$	2.31959	0.113864
$416$	0	0
$417$	2.71379	0.132895
$418$	4.54825i	0.222462i
$419$	0.955395	0.0466741	0.0233370	−	0.999728i	$-0.492571\pi$
$419$	0.955395	0.0466741	0.0233370	+	0.999728i	$0.492571\pi$
$420$	−1.44504	−0.0705108
$421$	5.68233i	0.276940i	0.990367	+	0.138470i	$0.0442184\pi$
$421$	5.68233i	0.276940i	−0.990367	+	0.138470i	$0.955782\pi$
$422$	− 12.5375i	− 0.610316i
$423$	− 1.78017i	− 0.0865547i
$424$	− 10.4112i	− 0.505612i
$425$	10.2220	0.495838
$426$	−11.4819	−0.556299
$427$	12.5918i	0.609360i
$428$	4.26875	0.206338
$429$	0	0
$430$	−2.23921	−0.107984
$431$	14.8465i	0.715133i	0.933888	+	0.357566i	$0.116393\pi$
$431$	14.8465i	0.715133i	−0.933888	+	0.357566i	$0.883607\pi$
$432$	1.00000	0.0481125
$433$	26.1497	1.25668	0.628338	−	0.777940i	$-0.283735\pi$
$433$	26.1497	1.25668	0.628338	+	0.777940i	$0.283735\pi$
$434$	− 43.6872i	− 2.09705i
$435$	3.03923i	0.145720i
$436$	6.21983i	0.297876i
$437$	42.3672i	2.02670i
$438$	0.533188	0.0254767
$439$	23.5502	1.12399	0.561994	−	0.827141i	$-0.310034\pi$
$439$	23.5502	1.12399	0.561994	+	0.827141i	$0.310034\pi$
$440$	0.325437i	0.0155146i
$441$	−9.39373	−0.447321
$442$	0	0
$443$	21.9433	1.04256	0.521279	−	0.853386i	$-0.325455\pi$
$443$	21.9433	1.04256	0.521279	+	0.853386i	$0.325455\pi$
$444$	− 0.615957i	− 0.0292320i
$445$	−2.31767	−0.109868
$446$	−5.42758	−0.257004
$447$	− 14.7356i	− 0.696968i
$448$	4.04892i	0.191293i
$449$	11.4034i	0.538161i	0.963118	+	0.269080i	$0.0867197\pi$
$449$	11.4034i	0.538161i	−0.963118	+	0.269080i	$0.913280\pi$
$450$	4.87263i	0.229698i
$451$	6.93362	0.326492
$452$	−12.9879	−0.610900
$453$	15.8213i	0.743350i
$454$	−16.5767	−0.777984
$455$	0	0
$456$	−4.98792	−0.233581
$457$	− 7.66919i	− 0.358749i	−0.983781	−	0.179375i	$-0.942593\pi$
$457$	− 7.66919i	− 0.358749i	0.983781	−	0.179375i	$-0.0574074\pi$
$458$	−23.8780	−1.11575
$459$	2.09783	0.0979185
$460$	3.03146i	0.141343i
$461$	28.5080i	1.32775i	0.747844	+	0.663874i	$0.231089\pi$
$461$	28.5080i	1.32775i	−0.747844	+	0.663874i	$0.768911\pi$
$462$	3.69202i	0.171768i
$463$	− 14.3284i	− 0.665898i	−0.942945	−	0.332949i	$-0.891956\pi$
$463$	− 14.3284i	− 0.665898i	0.942945	−	0.332949i	$-0.108044\pi$
$464$	8.51573	0.395333
$465$	3.85086	0.178579
$466$	− 13.9952i	− 0.648316i
$467$	−33.3207	−1.54190	−0.770948	−	0.636898i	$-0.780217\pi$
$467$	−33.3207	−1.54190	−0.770948	+	0.636898i	$0.780217\pi$
$468$	0	0
$469$	54.9831	2.53889
$470$	0.635334i	0.0293058i
$471$	−4.27413	−0.196941
$472$	6.04892	0.278424
$473$	5.72109i	0.263056i
$474$	− 11.7071i	− 0.537724i
$475$	− 24.3043i	− 1.11516i
$476$	8.49396i	0.389320i
$477$	10.4112	0.476696
$478$	−13.2862	−0.607697
$479$	− 22.1280i	− 1.01105i	−0.862811	−	0.505526i	$-0.831298\pi$
$479$	− 22.1280i	− 1.01105i	0.862811	−	0.505526i	$-0.168702\pi$
$480$	−0.356896	−0.0162900
$481$	0	0
$482$	10.4789	0.477301
$483$	34.3913i	1.56486i
$484$	−10.1685	−0.462206
$485$	0.699791	0.0317759
$486$	1.00000i	0.0453609i
$487$	0.126310i	0.00572364i	0.999996	+	0.00286182i	$0.000910947\pi$
$487$	0.126310i	0.00572364i	−0.999996	+	0.00286182i	$0.999089\pi$
$488$	3.10992i	0.140779i
$489$	0.317667i	0.0143654i
$490$	3.35258	0.151454
$491$	−13.9433	−0.629253	−0.314626	−	0.949216i	$-0.601879\pi$
$491$	−13.9433	−0.629253	−0.314626	+	0.949216i	$0.601879\pi$
$492$	7.60388i	0.342809i
$493$	17.8646	0.804581
$494$	0	0
$495$	−0.325437	−0.0146273
$496$	− 10.7899i	− 0.484479i
$497$	46.4892	2.08532
$498$	6.49934	0.291242
$499$	− 28.3913i	− 1.27097i	−0.772113	−	0.635485i	$-0.780800\pi$
$499$	− 28.3913i	− 1.27097i	0.772113	−	0.635485i	$-0.219200\pi$
$500$	− 3.52350i	− 0.157576i
$501$	− 12.3612i	− 0.552258i
$502$	− 3.48725i	− 0.155644i
$503$	12.5676	0.560363	0.280181	−	0.959947i	$-0.409605\pi$
$503$	12.5676	0.560363	0.280181	+	0.959947i	$0.409605\pi$
$504$	−4.04892	−0.180353
$505$	− 2.49204i	− 0.110894i
$506$	7.74525	0.344318
$507$	0	0
$508$	9.22282	0.409196
$509$	− 4.37675i	− 0.193996i	−0.995285	−	0.0969980i	$-0.969076\pi$
$509$	− 4.37675i	− 0.193996i	0.995285	−	0.0969980i	$-0.0309240\pi$
$510$	−0.748709	−0.0331534
$511$	−2.15883	−0.0955012
$512$	1.00000i	0.0441942i
$513$	− 4.98792i	− 0.220222i
$514$	− 6.53750i	− 0.288357i
$515$	− 1.76617i	− 0.0778266i
$516$	−6.27413	−0.276203
$517$	1.62325	0.0713906
$518$	2.49396i	0.109578i
$519$	17.0640	0.749026
$520$	0	0
$521$	−23.2707	−1.01951	−0.509753	−	0.860321i	$-0.670263\pi$
$521$	−23.2707	−1.01951	−0.509753	+	0.860321i	$0.670263\pi$
$522$	8.51573i	0.372723i
$523$	37.9952	1.66141	0.830707	−	0.556709i	$-0.187936\pi$
$523$	37.9952	1.66141	0.830707	+	0.556709i	$0.187936\pi$
$524$	14.5526	0.635732
$525$	− 19.7289i	− 0.861038i
$526$	8.01938i	0.349661i
$527$	− 22.6353i	− 0.986011i
$528$	0.911854i	0.0396834i
$529$	49.1473	2.13684
$530$	−3.71571	−0.161400
$531$	6.04892i	0.262501i
$532$	20.1957	0.875593
$533$	0	0
$534$	−6.49396	−0.281021
$535$	− 1.52350i	− 0.0658666i
$536$	13.5797	0.586554
$537$	24.9681	1.07745
$538$	− 27.6732i	− 1.19308i
$539$	− 8.56571i	− 0.368951i
$540$	− 0.356896i	− 0.0153584i
$541$	3.16421i	0.136040i	0.997684	+	0.0680200i	$0.0216682\pi$
$541$	3.16421i	0.136040i	−0.997684	+	0.0680200i	$0.978332\pi$
$542$	14.7289	0.632659
$543$	−5.26205	−0.225816
$544$	2.09783i	0.0899439i
$545$	2.21983	0.0950872
$546$	0	0
$547$	7.56033	0.323257	0.161628	−	0.986852i	$-0.448325\pi$
$547$	7.56033	0.323257	0.161628	+	0.986852i	$0.448325\pi$
$548$	− 15.4034i	− 0.658002i
$549$	−3.10992	−0.132728
$550$	−4.44312	−0.189455
$551$	− 42.4758i	− 1.80953i
$552$	8.49396i	0.361527i
$553$	47.4010i	2.01570i
$554$	− 3.26205i	− 0.138591i
$555$	−0.219833	−0.00933137
$556$	−2.71379	−0.115090
$557$	− 0.415502i	− 0.0176054i	−0.999961	−	0.00880269i	$-0.997198\pi$
$557$	− 0.415502i	− 0.0176054i	0.999961	−	0.00880269i	$-0.00280202\pi$
$558$	10.7899	0.456771
$559$	0	0
$560$	1.44504	0.0610642
$561$	1.91292i	0.0807635i
$562$	7.72587	0.325896
$563$	29.0465	1.22417	0.612083	−	0.790794i	$-0.290332\pi$
$563$	29.0465	1.22417	0.612083	+	0.790794i	$0.290332\pi$
$564$	1.78017i	0.0749586i
$565$	4.63533i	0.195010i
$566$	19.7802i	0.831422i
$567$	− 4.04892i	− 0.170039i
$568$	11.4819	0.481769
$569$	−39.6862	−1.66373	−0.831865	−	0.554977i	$-0.812727\pi$
$569$	−39.6862	−1.66373	−0.831865	+	0.554977i	$0.812727\pi$
$570$	1.78017i	0.0745630i
$571$	7.09651	0.296980	0.148490	−	0.988914i	$-0.452559\pi$
$571$	7.09651	0.296980	0.148490	+	0.988914i	$0.452559\pi$
$572$	0	0
$573$	10.5375	0.440210
$574$	− 30.7875i	− 1.28504i
$575$	−41.3879	−1.72599
$576$	−1.00000	−0.0416667
$577$	8.78687i	0.365802i	0.983131	+	0.182901i	$0.0585488\pi$
$577$	8.78687i	0.365802i	−0.983131	+	0.182901i	$0.941451\pi$
$578$	− 12.5991i	− 0.524053i
$579$	− 3.42758i	− 0.142446i
$580$	− 3.03923i	− 0.126197i
$581$	−26.3153	−1.09174
$582$	1.96077	0.0812766
$583$	9.49349i	0.393180i
$584$	−0.533188	−0.0220635
$585$	0	0
$586$	−12.9119	−0.533384
$587$	36.7066i	1.51504i	0.652810	+	0.757522i	$0.273590\pi$
$587$	36.7066i	1.51504i	−0.652810	+	0.757522i	$0.726410\pi$
$588$	9.39373	0.387391
$589$	−53.8189	−2.21757
$590$	− 2.15883i	− 0.0888778i
$591$	3.77479i	0.155274i
$592$	0.615957i	0.0253157i
$593$	− 10.8310i	− 0.444776i	−0.974958	−	0.222388i	$-0.928615\pi$
$593$	− 10.8310i	− 0.444776i	0.974958	−	0.222388i	$-0.0713852\pi$
$594$	−0.911854	−0.0374138
$595$	3.03146	0.124278
$596$	14.7356i	0.603592i
$597$	−17.9541	−0.734811
$598$	0	0
$599$	23.5254	0.961223	0.480611	−	0.876934i	$-0.340415\pi$
$599$	23.5254	0.961223	0.480611	+	0.876934i	$0.340415\pi$
$600$	− 4.87263i	− 0.198924i
$601$	27.8213	1.13486	0.567428	−	0.823423i	$-0.307939\pi$
$601$	27.8213	1.13486	0.567428	+	0.823423i	$0.307939\pi$
$602$	25.4034	1.03537
$603$	13.5797i	0.553009i
$604$	− 15.8213i	− 0.643760i
$605$	3.62910i	0.147544i
$606$	− 6.98254i	− 0.283646i
$607$	0.0972437	0.00394700	0.00197350	−	0.999998i	$-0.499372\pi$
$607$	0.0972437	0.00394700	0.00197350	+	0.999998i	$0.499372\pi$
$608$	4.98792	0.202287
$609$	− 34.4795i	− 1.39718i
$610$	1.10992	0.0449392
$611$	0	0
$612$	−2.09783	−0.0847999
$613$	− 8.06505i	− 0.325744i	−0.986647	−	0.162872i	$-0.947924\pi$
$613$	− 8.06505i	− 0.325744i	0.986647	−	0.162872i	$-0.0520758\pi$
$614$	19.9651	0.805725
$615$	2.71379	0.109431
$616$	− 3.69202i	− 0.148756i
$617$	19.2185i	0.773708i	0.922141	+	0.386854i	$0.126438\pi$
$617$	19.2185i	0.773708i	−0.922141	+	0.386854i	$0.873562\pi$
$618$	− 4.94869i	− 0.199065i
$619$	12.3827i	0.497703i	0.968542	+	0.248852i	$0.0800532\pi$
$619$	12.3827i	0.497703i	−0.968542	+	0.248852i	$0.919947\pi$
$620$	−3.85086	−0.154654
$621$	−8.49396	−0.340851
$622$	− 13.4819i	− 0.540574i
$623$	26.2935	1.05343
$624$	0	0
$625$	23.1056	0.924224
$626$	12.9245i	0.516568i
$627$	4.54825	0.181640
$628$	4.27413	0.170556
$629$	1.29218i	0.0515224i
$630$	1.44504i	0.0575718i
$631$	− 4.74333i	− 0.188829i	−0.995533	−	0.0944145i	$-0.969902\pi$
$631$	− 4.74333i	− 0.188829i	0.995533	−	0.0944145i	$-0.0300979\pi$
$632$	11.7071i	0.465683i
$633$	−12.5375	−0.498321
$634$	11.8726	0.471522
$635$	− 3.29159i	− 0.130623i
$636$	−10.4112	−0.412831
$637$	0	0
$638$	−7.76510	−0.307423
$639$	11.4819i	0.454216i
$640$	0.356896	0.0141075
$641$	16.4456	0.649563	0.324782	−	0.945789i	$-0.394709\pi$
$641$	16.4456	0.649563	0.324782	+	0.945789i	$0.394709\pi$
$642$	− 4.26875i	− 0.168474i
$643$	− 1.74525i	− 0.0688260i	−0.999408	−	0.0344130i	$-0.989044\pi$
$643$	− 1.74525i	− 0.0688260i	0.999408	−	0.0344130i	$-0.0109562\pi$
$644$	− 34.3913i	− 1.35521i
$645$	2.23921i	0.0881688i
$646$	10.4638	0.411694
$647$	−28.7633	−1.13080	−0.565401	−	0.824816i	$-0.691279\pi$
$647$	−28.7633	−1.13080	−0.565401	+	0.824816i	$0.691279\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−5.51573	−0.216511
$650$	0	0
$651$	−43.6872	−1.71224
$652$	− 0.317667i	− 0.0124408i
$653$	−16.1661	−0.632630	−0.316315	−	0.948654i	$-0.602446\pi$
$653$	−16.1661	−0.632630	−0.316315	+	0.948654i	$0.602446\pi$
$654$	6.21983	0.243215
$655$	− 5.19375i	− 0.202937i
$656$	− 7.60388i	− 0.296881i
$657$	− 0.533188i	− 0.0208016i
$658$	− 7.20775i	− 0.280987i
$659$	−16.3558	−0.637133	−0.318566	−	0.947901i	$-0.603201\pi$
$659$	−16.3558	−0.637133	−0.318566	+	0.947901i	$0.603201\pi$
$660$	0.325437	0.0126676
$661$	− 33.1159i	− 1.28806i	−0.765001	−	0.644029i	$-0.777261\pi$
$661$	− 33.1159i	− 1.28806i	0.765001	−	0.644029i	$-0.222739\pi$
$662$	−10.2392	−0.397958
$663$	0	0
$664$	−6.49934	−0.252223
$665$	− 7.20775i	− 0.279505i
$666$	−0.615957	−0.0238679
$667$	−72.3323	−2.80072
$668$	12.3612i	0.478269i
$669$	5.42758i	0.209843i
$670$	− 4.84654i	− 0.187238i
$671$	− 2.83579i	− 0.109474i
$672$	4.04892	0.156190
$673$	35.1540	1.35509	0.677544	−	0.735482i	$-0.263044\pi$
$673$	35.1540	1.35509	0.677544	+	0.735482i	$0.263044\pi$
$674$	− 1.44935i	− 0.0558270i
$675$	4.87263	0.187547
$676$	0	0
$677$	23.7855	0.914153	0.457076	−	0.889427i	$-0.348897\pi$
$677$	23.7855	0.914153	0.457076	+	0.889427i	$0.348897\pi$
$678$	12.9879i	0.498798i
$679$	−7.93900	−0.304671
$680$	0.748709	0.0287117
$681$	16.5767i	0.635222i
$682$	9.83877i	0.376746i
$683$	2.99223i	0.114495i	0.998360	+	0.0572473i	$0.0182323\pi$
$683$	2.99223i	0.114495i	−0.998360	+	0.0572473i	$0.981768\pi$
$684$	4.98792i	0.190718i
$685$	−5.49742	−0.210046
$686$	−9.69202	−0.370043
$687$	23.8780i	0.911003i
$688$	6.27413	0.239199
$689$	0	0
$690$	3.03146	0.115406
$691$	− 11.6233i	− 0.442169i	−0.975255	−	0.221085i	$-0.929040\pi$
$691$	− 11.6233i	− 0.442169i	0.975255	−	0.221085i	$-0.0709597\pi$
$692$	−17.0640	−0.648675
$693$	3.69202	0.140248
$694$	6.84117i	0.259687i
$695$	0.968541i	0.0367389i
$696$	− 8.51573i	− 0.322788i
$697$	− 15.9517i	− 0.604213i
$698$	−34.3370	−1.29968
$699$	−13.9952	−0.529348
$700$	19.7289i	0.745681i
$701$	33.8431	1.27824	0.639118	−	0.769109i	$-0.279300\pi$
$701$	33.8431	1.27824	0.639118	+	0.769109i	$0.279300\pi$
$702$	0	0
$703$	3.07234	0.115876
$704$	− 0.911854i	− 0.0343668i
$705$	0.635334	0.0239281
$706$	−26.0495	−0.980386
$707$	28.2717i	1.06327i
$708$	− 6.04892i	− 0.227332i
$709$	− 26.1909i	− 0.983619i	−0.870703	−	0.491810i	$-0.836336\pi$
$709$	− 26.1909i	− 0.983619i	0.870703	−	0.491810i	$-0.163664\pi$
$710$	− 4.09783i	− 0.153789i
$711$	−11.7071	−0.439050
$712$	6.49396	0.243371
$713$	91.6486i	3.43227i
$714$	8.49396	0.317878
$715$	0	0
$716$	−24.9681	−0.933100
$717$	13.2862i	0.496183i
$718$	8.49396	0.316992
$719$	21.7345	0.810560	0.405280	−	0.914193i	$-0.367174\pi$
$719$	21.7345	0.810560	0.405280	+	0.914193i	$0.367174\pi$
$720$	0.356896i	0.0133007i
$721$	20.0368i	0.746211i
$722$	− 5.87933i	− 0.218806i
$723$	− 10.4789i	− 0.389714i
$724$	5.26205	0.195562
$725$	41.4940	1.54105
$726$	10.1685i	0.377389i
$727$	2.01400	0.0746951	0.0373476	−	0.999302i	$-0.488109\pi$
$727$	2.01400	0.0746951	0.0373476	+	0.999302i	$0.488109\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.190293i	0.00704304i
$731$	13.1621	0.486817
$732$	3.10992	0.114946
$733$	− 13.5013i	− 0.498680i	−0.968416	−	0.249340i	$-0.919786\pi$
$733$	− 13.5013i	− 0.498680i	0.968416	−	0.249340i	$-0.0802137\pi$
$734$	27.4523i	1.01328i
$735$	− 3.35258i	− 0.123662i
$736$	− 8.49396i	− 0.313091i
$737$	−12.3827	−0.456123
$738$	7.60388	0.279903
$739$	− 16.5918i	− 0.610339i	−0.952298	−	0.305170i	$-0.901287\pi$
$739$	− 16.5918i	− 0.610339i	0.952298	−	0.305170i	$-0.0987131\pi$
$740$	0.219833	0.00808120
$741$	0	0
$742$	42.1540	1.54752
$743$	19.8479i	0.728148i	0.931370	+	0.364074i	$0.118614\pi$
$743$	19.8479i	0.728148i	−0.931370	+	0.364074i	$0.881386\pi$
$744$	−10.7899	−0.395575
$745$	5.25906	0.192677
$746$	26.6219i	0.974698i
$747$	− 6.49934i	− 0.237798i
$748$	− 1.91292i	− 0.0699432i
$749$	17.2838i	0.631537i
$750$	−3.52350	−0.128660
$751$	−27.9347	−1.01935	−0.509676	−	0.860367i	$-0.670235\pi$
$751$	−27.9347	−1.01935	−0.509676	+	0.860367i	$0.670235\pi$
$752$	− 1.78017i	− 0.0649160i
$753$	−3.48725	−0.127083
$754$	0	0
$755$	−5.64656	−0.205499
$756$	4.04892i	0.147258i
$757$	−0.548253	−0.0199266	−0.00996330	−	0.999950i	$-0.503171\pi$
$757$	−0.548253	−0.0199266	−0.00996330	+	0.999950i	$0.503171\pi$
$758$	−11.6474	−0.423053
$759$	− 7.74525i	− 0.281135i
$760$	− 1.78017i	− 0.0645735i
$761$	1.97584i	0.0716240i	0.999359	+	0.0358120i	$0.0114018\pi$
$761$	1.97584i	0.0716240i	−0.999359	+	0.0358120i	$0.988598\pi$
$762$	− 9.22282i	− 0.334107i
$763$	−25.1836	−0.911707
$764$	−10.5375	−0.381233
$765$	0.748709i	0.0270696i
$766$	−10.5181	−0.380035
$767$	0	0
$768$	1.00000	0.0360844
$769$	− 28.6112i	− 1.03175i	−0.856665	−	0.515873i	$-0.827468\pi$
$769$	− 28.6112i	− 1.03175i	0.856665	−	0.515873i	$-0.172532\pi$
$770$	−1.31767	−0.0474854
$771$	−6.53750	−0.235442
$772$	3.42758i	0.123361i
$773$	− 52.5080i	− 1.88858i	−0.329114	−	0.944290i	$-0.606750\pi$
$773$	− 52.5080i	− 1.88858i	0.329114	−	0.944290i	$-0.393250\pi$
$774$	6.27413i	0.225519i
$775$	− 52.5749i	− 1.88855i
$776$	−1.96077	−0.0703876
$777$	2.49396	0.0894703
$778$	9.25965i	0.331975i
$779$	−37.9275	−1.35889
$780$	0	0
$781$	−10.4698	−0.374639
$782$	− 17.8189i	− 0.637203i
$783$	8.51573	0.304327
$784$	−9.39373	−0.335490
$785$	− 1.52542i	− 0.0544445i
$786$	− 14.5526i	− 0.519073i
$787$	23.6426i	0.842769i	0.906882	+	0.421384i	$0.138456\pi$
$787$	23.6426i	0.842769i	−0.906882	+	0.421384i	$0.861544\pi$
$788$	− 3.77479i	− 0.134471i
$789$	8.01938	0.285497
$790$	4.17821	0.148654
$791$	− 52.5870i	− 1.86978i
$792$	0.911854	0.0324013
$793$	0	0
$794$	14.5133	0.515059
$795$	3.71571i	0.131783i
$796$	17.9541	0.636365
$797$	−41.6558	−1.47552	−0.737762	−	0.675061i	$-0.764117\pi$
$797$	−41.6558	−1.47552	−0.737762	+	0.675061i	$0.764117\pi$
$798$	− 20.1957i	− 0.714919i
$799$	− 3.73450i	− 0.132117i
$800$	4.87263i	0.172273i
$801$	6.49396i	0.229453i
$802$	−38.8418	−1.37155
$803$	0.486189	0.0171573
$804$	− 13.5797i	− 0.478920i
$805$	−12.2741	−0.432606
$806$	0	0
$807$	−27.6732	−0.974144
$808$	6.98254i	0.245645i
$809$	−44.2392	−1.55537	−0.777684	−	0.628656i	$-0.783606\pi$
$809$	−44.2392	−1.55537	−0.777684	+	0.628656i	$0.783606\pi$
$810$	−0.356896	−0.0125400
$811$	52.3913i	1.83971i	0.392260	+	0.919854i	$0.371693\pi$
$811$	52.3913i	1.83971i	−0.392260	+	0.919854i	$0.628307\pi$
$812$	34.4795i	1.20999i
$813$	− 14.7289i	− 0.516564i
$814$	− 0.561663i	− 0.0196863i
$815$	−0.113374	−0.00397132
$816$	2.09783	0.0734389
$817$	− 31.2948i	− 1.09487i
$818$	−33.9221	−1.18606
$819$	0	0
$820$	−2.71379	−0.0947697
$821$	− 25.6276i	− 0.894408i	−0.894432	−	0.447204i	$-0.852420\pi$
$821$	− 25.6276i	− 0.894408i	0.894432	−	0.447204i	$-0.147580\pi$
$822$	−15.4034	−0.537256
$823$	40.2553	1.40321	0.701606	−	0.712565i	$-0.252466\pi$
$823$	40.2553	1.40321	0.701606	+	0.712565i	$0.252466\pi$
$824$	4.94869i	0.172396i
$825$	4.44312i	0.154690i
$826$	24.4916i	0.852171i
$827$	18.0519i	0.627726i	0.949468	+	0.313863i	$0.101623\pi$
$827$	18.0519i	0.627726i	−0.949468	+	0.313863i	$0.898377\pi$
$828$	8.49396	0.295185
$829$	−22.6655	−0.787204	−0.393602	−	0.919281i	$-0.628771\pi$
$829$	−22.6655	−0.787204	−0.393602	+	0.919281i	$0.628771\pi$
$830$	2.31959i	0.0805140i
$831$	−3.26205	−0.113159
$832$	0	0
$833$	−19.7065	−0.682790
$834$	2.71379i	0.0939709i
$835$	4.41166	0.152672
$836$	−4.54825	−0.157305
$837$	− 10.7899i	− 0.372952i
$838$	0.955395i	0.0330036i
$839$	− 22.0823i	− 0.762365i	−0.924500	−	0.381183i	$-0.875517\pi$
$839$	− 22.0823i	− 0.762365i	0.924500	−	0.381183i	$-0.124483\pi$
$840$	− 1.44504i	− 0.0498587i
$841$	43.5176	1.50061
$842$	−5.68233	−0.195826
$843$	− 7.72587i	− 0.266093i
$844$	12.5375	0.431559
$845$	0	0
$846$	1.78017	0.0612034
$847$	− 41.1715i	− 1.41467i
$848$	10.4112	0.357522
$849$	19.7802	0.678854
$850$	10.2220i	0.350610i
$851$	− 5.23191i	− 0.179348i
$852$	− 11.4819i	− 0.393363i
$853$	− 28.9831i	− 0.992364i	−0.868219	−	0.496182i	$-0.834735\pi$
$853$	− 28.9831i	− 0.992364i	0.868219	−	0.496182i	$-0.165265\pi$
$854$	−12.5918	−0.430882
$855$	1.78017	0.0608804
$856$	4.26875i	0.145903i
$857$	42.9047	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$857$	42.9047	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$858$	0	0
$859$	−47.0616	−1.60572	−0.802860	−	0.596167i	$-0.796690\pi$
$859$	−47.0616	−1.60572	−0.802860	+	0.596167i	$0.796690\pi$
$860$	− 2.23921i	− 0.0763564i
$861$	−30.7875	−1.04923
$862$	−14.8465	−0.505675
$863$	42.6064i	1.45034i	0.688571	+	0.725169i	$0.258238\pi$
$863$	42.6064i	1.45034i	−0.688571	+	0.725169i	$0.741762\pi$
$864$	1.00000i	0.0340207i
$865$	6.09006i	0.207068i
$866$	26.1497i	0.888604i
$867$	−12.5991	−0.427888
$868$	43.6872	1.48284
$869$	− 10.6752i	− 0.362130i
$870$	−3.03923	−0.103040
$871$	0	0
$872$	−6.21983	−0.210630
$873$	− 1.96077i	− 0.0663621i
$874$	−42.3672	−1.43309
$875$	14.2664	0.482291
$876$	0.533188i	0.0180147i
$877$	− 27.4082i	− 0.925509i	−0.886486	−	0.462755i	$-0.846861\pi$
$877$	− 27.4082i	− 0.925509i	0.886486	−	0.462755i	$-0.153139\pi$
$878$	23.5502i	0.794780i
$879$	12.9119i	0.435506i
$880$	−0.325437	−0.0109705
$881$	−24.3177	−0.819283	−0.409642	−	0.912247i	$-0.634346\pi$
$881$	−24.3177	−0.819283	−0.409642	+	0.912247i	$0.634346\pi$
$882$	− 9.39373i	− 0.316303i
$883$	32.2306	1.08465	0.542323	−	0.840170i	$-0.317545\pi$
$883$	32.2306	1.08465	0.542323	+	0.840170i	$0.317545\pi$
$884$	0	0
$885$	−2.15883	−0.0725684
$886$	21.9433i	0.737200i
$887$	−35.1642	−1.18070	−0.590349	−	0.807148i	$-0.701010\pi$
$887$	−35.1642	−1.18070	−0.590349	+	0.807148i	$0.701010\pi$
$888$	0.615957	0.0206702
$889$	37.3424i	1.25242i
$890$	− 2.31767i	− 0.0776884i
$891$	0.911854i	0.0305483i
$892$	− 5.42758i	− 0.181729i
$893$	−8.87933	−0.297135
$894$	14.7356	0.492831
$895$	8.91100i	0.297862i
$896$	−4.04892	−0.135265
$897$	0	0
$898$	−11.4034	−0.380537
$899$	− 91.8835i	− 3.06449i
$900$	−4.87263	−0.162421
$901$	21.8410	0.727628
$902$	6.93362i	0.230864i
$903$	− 25.4034i	− 0.845373i
$904$	− 12.9879i	− 0.431972i
$905$	− 1.87800i	− 0.0624269i
$906$	−15.8213	−0.525628
$907$	13.1207	0.435665	0.217832	−	0.975986i	$-0.430101\pi$
$907$	13.1207	0.435665	0.217832	+	0.975986i	$0.430101\pi$
$908$	− 16.5767i	− 0.550118i
$909$	−6.98254	−0.231596
$910$	0	0
$911$	45.7453	1.51561	0.757804	−	0.652482i	$-0.226272\pi$
$911$	45.7453	1.51561	0.757804	+	0.652482i	$0.226272\pi$
$912$	− 4.98792i	− 0.165166i
$913$	5.92645	0.196137
$914$	7.66919	0.253674
$915$	− 1.10992i	− 0.0366927i
$916$	− 23.8780i	− 0.788951i
$917$	58.9221i	1.94578i
$918$	2.09783i	0.0692389i
$919$	17.9849	0.593268	0.296634	−	0.954991i	$-0.404136\pi$
$919$	17.9849	0.593268	0.296634	+	0.954991i	$0.404136\pi$
$920$	−3.03146	−0.0999442
$921$	− 19.9651i	− 0.657872i
$922$	−28.5080	−0.938860
$923$	0	0
$924$	−3.69202	−0.121459
$925$	3.00133i	0.0986831i
$926$	14.3284	0.470861
$927$	−4.94869	−0.162536
$928$	8.51573i	0.279543i
$929$	− 31.6883i	− 1.03966i	−0.854270	−	0.519830i	$-0.825995\pi$
$929$	− 31.6883i	− 1.03966i	0.854270	−	0.519830i	$-0.174005\pi$
$930$	3.85086i	0.126275i
$931$	46.8552i	1.53562i
$932$	13.9952	0.458428
$933$	−13.4819	−0.441377
$934$	− 33.3207i	− 1.09029i
$935$	−0.682713	−0.0223271
$936$	0	0
$937$	−53.0484	−1.73302	−0.866509	−	0.499162i	$-0.833641\pi$
$937$	−53.0484	−1.73302	−0.866509	+	0.499162i	$0.833641\pi$
$938$	54.9831i	1.79526i
$939$	12.9245	0.421776
$940$	−0.635334	−0.0207223
$941$	− 21.9433i	− 0.715332i	−0.933850	−	0.357666i	$-0.883573\pi$
$941$	− 21.9433i	− 0.715332i	0.933850	−	0.357666i	$-0.116427\pi$
$942$	− 4.27413i	− 0.139259i
$943$	64.5870i	2.10324i
$944$	6.04892i	0.196875i
$945$	1.44504	0.0470072
$946$	−5.72109	−0.186009
$947$	12.2241i	0.397231i	0.980077	+	0.198616i	$0.0636445\pi$
$947$	12.2241i	0.397231i	−0.980077	+	0.198616i	$0.936355\pi$
$948$	11.7071	0.380229
$949$	0	0
$950$	24.3043	0.788534
$951$	− 11.8726i	− 0.384996i
$952$	−8.49396	−0.275291
$953$	3.85862	0.124993	0.0624966	−	0.998045i	$-0.480094\pi$
$953$	3.85862	0.124993	0.0624966	+	0.998045i	$0.480094\pi$
$954$	10.4112i	0.337075i
$955$	3.76079i	0.121696i
$956$	− 13.2862i	− 0.429707i
$957$	7.76510i	0.251010i
$958$	22.1280	0.714922
$959$	62.3672	2.01394
$960$	− 0.356896i	− 0.0115188i
$961$	−85.4210	−2.75552
$962$	0	0
$963$	−4.26875	−0.137559
$964$	10.4789i	0.337502i
$965$	1.22329	0.0393791
$966$	−34.3913	−1.10652
$967$	0.613564i	0.0197309i	0.999951	+	0.00986545i	$0.00314032\pi$
$967$	0.613564i	0.0197309i	−0.999951	+	0.00986545i	$0.996860\pi$
$968$	− 10.1685i	− 0.326829i
$969$	− 10.4638i	− 0.336147i
$970$	0.699791i	0.0224689i
$971$	−12.9769	−0.416449	−0.208224	−	0.978081i	$-0.566768\pi$
$971$	−12.9769	−0.416449	−0.208224	+	0.978081i	$0.566768\pi$
$972$	−1.00000	−0.0320750
$973$	− 10.9879i	− 0.352256i
$974$	−0.126310	−0.00404722
$975$	0	0
$976$	−3.10992	−0.0995460
$977$	37.0616i	1.18571i	0.805311	+	0.592853i	$0.201998\pi$
$977$	37.0616i	1.18571i	−0.805311	+	0.592853i	$0.798002\pi$
$978$	−0.317667	−0.0101579
$979$	−5.92154	−0.189253
$980$	3.35258i	0.107094i
$981$	− 6.21983i	− 0.198584i
$982$	− 13.9433i	− 0.444949i
$983$	− 14.1193i	− 0.450337i	−0.974320	−	0.225169i	$-0.927707\pi$
$983$	− 14.1193i	− 0.450337i	0.974320	−	0.225169i	$-0.0722933\pi$
$984$	−7.60388	−0.242403
$985$	−1.34721	−0.0429256
$986$	17.8646i	0.568925i
$987$	−7.20775	−0.229425
$988$	0	0
$989$	−53.2922	−1.69459
$990$	− 0.325437i	− 0.0103431i
$991$	28.5392	0.906576	0.453288	−	0.891364i	$-0.350251\pi$
$991$	28.5392	0.906576	0.453288	+	0.891364i	$0.350251\pi$
$992$	10.7899	0.342578
$993$	10.2392i	0.324932i
$994$	46.4892i	1.47455i
$995$	− 6.40773i	− 0.203139i
$996$	6.49934i	0.205939i
$997$	−18.8853	−0.598103	−0.299052	−	0.954237i	$-0.596670\pi$
$997$	−18.8853	−0.598103	−0.299052	+	0.954237i	$0.596670\pi$
$998$	28.3913	0.898712
$999$	0.615957i	0.0194880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.b.g.337.5		6
3.2	odd	2		3042.2.b.r.1351.2		6
13.2	odd	12		1014.2.e.k.529.2		6
13.3	even	3		1014.2.i.g.823.2		12
13.4	even	6		1014.2.i.g.361.2		12
13.5	odd	4		1014.2.a.o.1.2	yes	3
13.6	odd	12		1014.2.e.k.991.2		6
13.7	odd	12		1014.2.e.m.991.2		6
13.8	odd	4		1014.2.a.m.1.2	✓	3
13.9	even	3		1014.2.i.g.361.5		12
13.10	even	6		1014.2.i.g.823.5		12
13.11	odd	12		1014.2.e.m.529.2		6
13.12	even	2	inner	1014.2.b.g.337.2		6
39.5	even	4		3042.2.a.bd.1.2		3
39.8	even	4		3042.2.a.be.1.2		3
39.38	odd	2		3042.2.b.r.1351.5		6
52.31	even	4		8112.2.a.bz.1.2		3
52.47	even	4		8112.2.a.ce.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.2	✓	3	13.8	odd	4
1014.2.a.o.1.2	yes	3	13.5	odd	4
1014.2.b.g.337.2		6	13.12	even	2	inner
1014.2.b.g.337.5		6	1.1	even	1	trivial
1014.2.e.k.529.2		6	13.2	odd	12
1014.2.e.k.991.2		6	13.6	odd	12
1014.2.e.m.529.2		6	13.11	odd	12
1014.2.e.m.991.2		6	13.7	odd	12
1014.2.i.g.361.2		12	13.4	even	6
1014.2.i.g.361.5		12	13.9	even	3
1014.2.i.g.823.2		12	13.3	even	3
1014.2.i.g.823.5		12	13.10	even	6
3042.2.a.bd.1.2		3	39.5	even	4
3042.2.a.be.1.2		3	39.8	even	4
3042.2.b.r.1351.2		6	3.2	odd	2
3042.2.b.r.1351.5		6	39.38	odd	2
8112.2.a.bz.1.2		3	52.31	even	4
8112.2.a.ce.1.2		3	52.47	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +0.356896i q^{5} +1.00000i q^{6} -4.04892i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +0.356896i q^{5} +1.00000i q^{6} -4.04892i q^{7} -1.00000i q^{8} +1.00000 q^{9} -0.356896 q^{10} +0.911854i q^{11} -1.00000 q^{12} +4.04892 q^{14} +0.356896i q^{15} +1.00000 q^{16} +2.09783 q^{17} +1.00000i q^{18} -4.98792i q^{19} -0.356896i q^{20} -4.04892i q^{21} -0.911854 q^{22} -8.49396 q^{23} -1.00000i q^{24} +4.87263 q^{25} +1.00000 q^{27} +4.04892i q^{28} +8.51573 q^{29} -0.356896 q^{30} -10.7899i q^{31} +1.00000i q^{32} +0.911854i q^{33} +2.09783i q^{34} +1.44504 q^{35} -1.00000 q^{36} +0.615957i q^{37} +4.98792 q^{38} +0.356896 q^{40} -7.60388i q^{41} +4.04892 q^{42} +6.27413 q^{43} -0.911854i q^{44} +0.356896i q^{45} -8.49396i q^{46} -1.78017i q^{47} +1.00000 q^{48} -9.39373 q^{49} +4.87263i q^{50} +2.09783 q^{51} +10.4112 q^{53} +1.00000i q^{54} -0.325437 q^{55} -4.04892 q^{56} -4.98792i q^{57} +8.51573i q^{58} +6.04892i q^{59} -0.356896i q^{60} -3.10992 q^{61} +10.7899 q^{62} -4.04892i q^{63} -1.00000 q^{64} -0.911854 q^{66} +13.5797i q^{67} -2.09783 q^{68} -8.49396 q^{69} +1.44504i q^{70} +11.4819i q^{71} -1.00000i q^{72} -0.533188i q^{73} -0.615957 q^{74} +4.87263 q^{75} +4.98792i q^{76} +3.69202 q^{77} -11.7071 q^{79} +0.356896i q^{80} +1.00000 q^{81} +7.60388 q^{82} -6.49934i q^{83} +4.04892i q^{84} +0.748709i q^{85} +6.27413i q^{86} +8.51573 q^{87} +0.911854 q^{88} +6.49396i q^{89} -0.356896 q^{90} +8.49396 q^{92} -10.7899i q^{93} +1.78017 q^{94} +1.78017 q^{95} +1.00000i q^{96} -1.96077i q^{97} -9.39373i q^{98} +0.911854i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9	\( 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9} + 6 q^{10} - 6 q^{12} + 6 q^{14} + 6 q^{16} - 24 q^{17} + 2 q^{22} - 32 q^{23} - 4 q^{25} + 6 q^{27} + 26 q^{29} + 6 q^{30} + 8 q^{35} - 6 q^{36} - 8 q^{38} - 6 q^{40} + 6 q^{42} + 16 q^{43} + 6 q^{48} + 8 q^{49} - 24 q^{51} + 30 q^{53} - 44 q^{55} - 6 q^{56} - 20 q^{61} + 18 q^{62} - 6 q^{64} + 2 q^{66} + 24 q^{68} - 32 q^{69} - 24 q^{74} - 4 q^{75} + 12 q^{77} - 10 q^{79} + 6 q^{81} + 28 q^{82} + 26 q^{87} - 2 q^{88} + 6 q^{90} + 32 q^{92} + 8 q^{94} + 8 q^{95}+O(q^{100}) \) 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9 + 6 * q^10 - 6 * q^12 + 6 * q^14 + 6 * q^16 - 24 * q^17 + 2 * q^22 - 32 * q^23 - 4 * q^25 + 6 * q^27 + 26 * q^29 + 6 * q^30 + 8 * q^35 - 6 * q^36 - 8 * q^38 - 6 * q^40 + 6 * q^42 + 16 * q^43 + 6 * q^48 + 8 * q^49 - 24 * q^51 + 30 * q^53 - 44 * q^55 - 6 * q^56 - 20 * q^61 + 18 * q^62 - 6 * q^64 + 2 * q^66 + 24 * q^68 - 32 * q^69 - 24 * q^74 - 4 * q^75 + 12 * q^77 - 10 * q^79 + 6 * q^81 + 28 * q^82 + 26 * q^87 - 2 * q^88 + 6 * q^90 + 32 * q^92 + 8 * q^94 + 8 * q^95

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